Unlink Key frames of two objects
Select one of the objects and:


Click U (Make Single User) > Object Animation.
Or go in the Dopesheet window > Action Editor mode and press + (Create New Action)
Or as Edgel3D said, go to the Outliner, unfold the submenu under your object, you'll see Animation, right click > Clear Animation (in that case, the object won't even have anymore animation).